Contributions of the paper. This paper contributes to solving
the path following control problem for swimming helical microbots in
several ways. First, the paper develops an ILOS-based guidance
law for swimming microrobots, which is inspired from the automatic ship steering
literature [1]}, [2]}, [3]}. In the
presence of disturbances that drive the
microswimmer away from its desired path, embedding the integral
compensation dynamics will build up a corrective action in the reference vector field. Second,
using the ILOS-based guidance law, this paper casts the control input
computation as a trust-region subproblem (TRS), i.e., a quadratic program over a sphere,
which belongs to the wider class of real-time optimization-based controllers.
In our previous work [4]}, we also used the ODS framework for designing
path following controllers for magnetic helical microswimmers. While the proposed
ODS-based controller in [4]}, which is based on the traditional
line-of-sight (LOS) guidance law, respects the step-out frequencies, it relies on the full
knowledge of the microswimmer dynamical parameters and assumes absence of disturbances. Additionally,
the controller in [4]} formally guarantees neither the continuity of the control inputs nor the
continuity of the commanded desired-velocity profiles. In this paper, we relax many of our
prior assumptions.
